A similar result was proved by Kairouz et al. [1]} that holds only for sufficiently “small” (albeit unspecified) \(\varepsilon \)  and \(\delta = 0\) . When compared to Chernoff-Stein lemma [2]}, establishing \(D_{\mathsf {KL}}(P_0\Vert P_1)\)  as the asymptotic exponential decay rate of \(\beta _n^{\varepsilon , \delta }(\alpha )\) , the above corollary, once again, justifies the reduction of effective sample size from \(n\)  to \(\varphi (\varepsilon , \delta )n\)  in the presence of \((\varepsilon , \delta )\) -LDP requirement.
